Finite Group Databasebeta

← Group #339180

Character table — Group #339180

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488884444444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1
χ3111111111111111111111111-1-1111111111111111111-11-1-1-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-11
χ51111111111111111111111-1-111111111-1-11111-1-1-1-1-1-11-111-1-1-1-1-1-1-1-11-11
χ61111111111111111111111-1-111-1-1-1-11111-1-1-1-11111111-111-1-1-1-11111-1-1-1
χ71111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-111-111-1-1-1-111-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-111-111-1-111-1-11-1-1
χ11111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-111-11-1-1-1-111-1-111-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-1-1-1-1-1-111-111
χ13111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-11111-1-1-111
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-111-1-11111-1
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-111111-1-1111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11111111-1-1-1-11
χ17222222222-2-22-2-222-2-20000220022-2-200220000-2-200000-20000000000000
χ18222222222-2-22-2-222-2-200002200-2-22200-2-200002200000-20000000000000
χ19222222222-2-22-2-222-2-20000-2-20022-2-200-2-20000220000020000000000000
χ20222222222-2-22-2-222-2-20000-2-200-2-22200220000-2-20000020000000000000
χ2122222222-222-222-2-2-2-2222200220000-2-2000000000000-20-2200000000000
χ2222222222-222-222-2-2-2-2222200-2-20000-2-2000000000000202-200000000000
χ2322222222-222-222-2-2-2-2-2-2-2-2002200002200000000000020-2-200000000000
χ2422222222-222-222-2-2-2-2-2-2-2-200-2-2000022000000000000-202200000000000
χ2522-22-22-2-2-2-2-2222-22-22000000000000000022-2-200000000002i−2i002i−2i00000
χ2622-22-22-2-2-2-2-2222-22-22000000000000000022-2-20000000000−2i2i00−2i2i00000
χ2722-22-22-2-2-2-2-2222-22-220000000000000000-2-22200000000002i−2i00−2i2i00000
χ2822-22-22-2-2-2-2-2222-22-220000000000000000-2-2220000000000−2i2i002i−2i00000
χ292-2-222-22-2-2002002-200i2i2−i2−i22-200002i−2ii2−i2002−22−22i−2i22−2−2000000i2−i20000000
χ302-2-222-22-2-2002002-200i2i2−i2−i22-20000−2i2ii2−i200−22−22−2i2i−2−222000000i2−i20000000
χ312-2-222-22-2-2002002-200i2i2−i2−i2-2200002i−2ii2−i2002−22−2−2i2i−2−222000000−i2i20000000
χ322-2-222-22-2-2002002-200i2i2−i2−i2-220000−2i2ii2−i200−22−222i−2i22−2−2000000−i2i20000000
χ332-2-222-22-2-2002002-200−i2−i2i2i22-200002i−2i−i2i200−22−222i−2i−2−222000000−i2i20000000
χ342-2-222-22-2-2002002-200−i2−i2i2i22-20000−2i2i−i2i2002−22−2−2i2i22−2−2000000−i2i20000000
χ352-2-222-22-2-2002002-200−i2−i2i2i2-2200002i−2i−i2i200−22−22−2i2i22−2−2000000i2−i20000000
χ362-2-222-22-2-2002002-200−i2−i2i2i2-220000−2i2i−i2i2002−22−22i−2i−2−222000000i2−i20000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-44-4-4-404-404-4000000000000000000000000000000000000000022−22000
χ39444-44-4-4-404-404-40000000000000000000000000000000000000000−2222000
χ40444-44-4-4-40-440-4400000000004-4000000000000000000000000000000000
χ41444-44-4-4-40-440-440000000000-44000000000000000000000000000000000
χ4244-44-44-4-4444-4-4-44-4-4400000000000000000000000000000000000000000
χ4344-44-44-4-44-4-4-4444-44-400000000000000000000000000000000000000000
χ4444-44-44-4-4-4444-4-4-444-400000000000000000000000000000000000000000
χ4544-4-4-4-44404-40-44000000000000000000000000002i2−2i22i2−2i2000000000000000
χ4644-4-4-4-44404-40-4400000000000000000000000000−2i22i2−2i22i2000000000000000
χ4744-4-4-4-4440-4404-400004i−4i4i−4i0000000000000000000000000000000000000
χ4844-4-4-4-4440-4404-40000−4i4i−4i4i0000000000000000000000000000000000000
χ494-444-4-4-44400400-4-400000000000000000022−22−2222000000000000000000000
χ504-444-4-4-44400400-4-4000000000000000000−222222−22000000000000000000000
χ514-444-4-4-44-400-4004400000000004i−4i0000000000000000000000000000000
χ524-444-4-4-44-400-400440000000000−4i4i0000000000000000000000000000000
χ534-44-4-444-4000000000022−22−222200000000002i2−2i20000002i−2i−2i2i000000000000000
χ544-44-4-444-4000000000022−22−22220000000000−2i22i2000000−2i2i2i−2i000000000000000
χ554-44-4-444-40000000000−222222−2200000000002i2−2i2000000−2i2i2i−2i000000000000000
χ564-44-4-444-40000000000−222222−220000000000−2i22i20000002i−2i−2i2i000000000000000
χ574-4-444-44-4400-400-44002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ584-4-444-44-4400-400-4400−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ598-8-8-888-88000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).